Abstract
A new four way split method of bit-level Toeplitz matrix-vector product for computing trinomial-based multiplier over GF(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> ) is presented. The proposed scheme is based on two way splitting method to use Toeplitz matrix-vector product using inner product (TMVPIP) formula. Applying the proposed TMVPIP architecture, it is shown that the computation time of proposed sub quadratic multiplier can be reduced from O(log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> m) of the existing sub quadratic multipliers to O(log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> m). Our proposed sub quadratic multiplier with TMVPIP formula is suitable for efficient implementation of the point multiplication in Koblitz curves.
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